Theoretical analysis for photophoresis of a microscale hydrophobic particle in liquids

Abstract

In the present study, combining the conventional photothermal analysis and the concept of interaction of solvent molecules in interfacial layer used for thermophoresis in liquid, a theory for photophoresis of a hydrophobic particle suspended in liquids is developed. To characterize hydrophobicity of the micro-particle, slip length in Navier's formula is used as an index. Analytical expressions are derived and a parametric analysis for photophoretic velocity is performed with emphasis on the influences of particle characteristics such as size, optical properties, hydrophobicity, and thermal conductivity. Heat source function and the corresponding asymmetry factor at various conditions are evaluated to interpret the mechanisms of negative and positive photophoresis and the conditions for transition between them. The present theory discloses that the particle surface hydrophobicity or fluid slippage at particle-liquid interface may lead to a remarkable enhancement in the particle photophoretic velocity in liquids. Higher particle thermal conductivity and larger size of liquid molecules both result in weaker photophoretic motion.

Self-diffraction of continuous laser radiation in a disperse medium with absorbing particles

“…Mechanisms for the photophoretic action and means for their analysis are mainly developed for gaseous media [22,23]; the theory of photophoresis in liquids is not well elaborated and only a few attempts were made in this field [24,25]. For rough estimations, we use a simplified calculation scheme based on combination of approaches presented in Refs [23].…”

“…For rough estimations, we use a simplified calculation scheme based on combination of approaches presented in Refs [23]. and [25]. We start with Eq.…”

“…We start with Eq. (17) of Ref [25]. which gives the photophoresis velocity p V of a particle and define the corresponding photophoretic force p F via Stokes formula 6 ,…”

“…is the light absorption coefficient of the particle, and assume the particle to be nonhydrophobic (the 'slip length' s L in [25]). After some manipulations, the photophoretic force can be represented by the expression …”

“…(8) of Ref [23], which characterizes the momentum transfer from the liquid molecules to the particle with given properties, ( ) 0 P c n I = is the energy flow density in the incident light field supposed to be a plane wave in [25]. In Eq.…”